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What is the greatest number by which when 156, 181 and 331 are divided, the remainder is 6 in each case?

What is the greatest number by which when 156, 181 and 331 are divided, the remainder is 6 in each case? Correct Answer 25

Given:

The given numbers are 156, 181 and 331

After dividing by the greatest number, the remainder in each case = 6

Concept used:

The greatest number that will divide a, b, and c and leaving the same remainder in each case is given by the HCF of |a - b|, |b - c|, and |c - a|

Calculation:

Here, |156 - 181| = |- 25| = 25

|181 - 331| = |- 150| = 150

|331 - 156| = 175

Prime factors of 25 = 5 × 5

Prime factors of 150 = 2 × 3 × 5 × 5

Prime factors of 175 = 5 × 5 × 7

So, HCF of 25, 150, and 175 = 5 × 5 = 25

∴ The greatest number is 25

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